Math Skill: Simplifying Algebraic Expressions
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Simplifying Algebraic Expressions

To review algebraic terms, see here.

Simplify algebraic expressions by combining like terms.
Like terms are terms with the same variable or variables.

Like termsUnlike terms
All constants are like terms. Constants and variables are not like terms.
2, -34, 0.59, ¼ 18, x
All these terms have one variable, y. Terms with different variables are not like terms.
3y, -10y, y, 6y 7x, 7y
All these terms have the same variable, t3. Terms with the same variable but different exponents are not like terms.
t3, 9t3, ½t3, -14t3 10y, 3y2
All these terms have the same variable combination, xy. Terms with different variable combinations are not like terms.
29xy, 0.5xy, xy, -xy x, 8xy

Example 1: One variable

-x - 6 + 5x   Simplified:

-x and 5x are like terms, so combine them.
-x - 6 + 5x = 4x - 6

Example 2: Two variables

3y + 4 - y + 4x - 6   Simplified:

Combine the x and y terms and the constants.

 3y + 4 - y + 4x - 6 = 4x + (3y - y) + (4 - 6) = 4x + 2y + -2 =
This simplifies to 4x + 2y - 2

Example 3:

Simplify the expression and order your answer based on alphabetical letter and magnitude.
4x2 - 3y + x - 2x2 - 2 - 3y + 7   Simplified:

Combine the terms and simplify.

 4x2 - 3y + x - 2x2 - 2 - 3y + 7 = (4x2 - 2x2) + x + (-3y - 3y) + (-2 + 7) = 2x2 + x + (-6y) + 5 =
This simplifies to 2x2 + x - 6y + 5

### Complexity=3, Mode=one-var

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
 1.   - 7 + 5x - 2 Simplified: 2.   - 5x + 3 - 4x Simplified:

### Complexity=5, Mode=one-var

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
 1.   - 3x + 3x - 2 + 5x + 4 Simplified: 2.   -x + 6 - 3x - 2x + 7 Simplified:

### Complexity=5, Mode=two-vars

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
 1.   x - 4 - x - 5x + 3y Simplified: 2.   - 2x - 7 - 5x + 8 + y Simplified:

### Complexity=6, Mode=with-exp

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
 1.   - 5y 2 - 3x + 4y 2 + y - 4 - 3 Simplified: 2.   3x 2 + 3y - y 2 + 5y - y 2 - 5x Simplified:

### Complexity=7, Mode=with-exp

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
 1.   2y 2 + 4 - 7 + 3x - 4y - 3y + 4y Simplified: 2.   4x 2 + x 2 + 4y 2 + 4y + 7 + 3x + 2 Simplified:

### Complexity=2, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
 1.   -(1 + 3y) + 2(2y - 3) Simplified: 2.   -(5y - 8) - 2(6 + 3) Simplified:

### Complexity=3, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
 1.   1(- 2y + 3x) - 2(2 - 5) - 2(8 + 7) Simplified: 2.   -(5 + 6) - (3x + 3y) - 4(- 6 - 7) Simplified:

### Complexity=4, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
 1.   -(5 - 4y) - (- 3y - 2) - (- 5y + 5) - 3(- 4x - 2) Simplified: 2.   2(- 4y + 2y) - (5x - 2y) - (7 - 3) - (2x - x) Simplified:

### Complexity=5, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
 1.   3(5y - 4) - (- 4x - y) + 1(2x + 1) - (4y - 4y) + 1(-x - 4y) Simplified: 2.   - 4(-y - 5x) + 1(2y - 2y) - 2(- 5x + 3) + 4(- 4x - 3) - (3 + 3) Simplified:

### Complexity=3, Mode=one-var

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
1- 7 + 5x - 2
Simplified:
Solution
- 7 + - 2 = - 9
2- 5x + 3 - 4x
Simplified:
Solution
- 5x + - 4x = - 9x

### Complexity=5, Mode=one-var

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
1- 3x + 3x - 2 + 5x + 4
Simplified:
Solution
- 3x + 3x + 5x = 5x
- 2 + 4 = 2
2-x + 6 - 3x - 2x + 7
Simplified:
Solution
-x + - 3x + - 2x = - 6x
6 + 7 = 13

### Complexity=5, Mode=two-vars

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
1x - 4 - x - 5x + 3y
Simplified:
Solution
x + -x + - 5x = - 5x
2- 2x - 7 - 5x + 8 + y
Simplified:
Solution
- 2x + - 5x = - 7x
- 7 + 8 = 1

### Complexity=6, Mode=with-exp

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
1- 5y 2 - 3x + 4y 2 + y - 4 - 3
Simplified:
Solution
- 5y 2 + 4y 2 = -y 2
- 4 + - 3 = - 7
23x 2 + 3y - y 2 + 5y - y 2 - 5x
Simplified:
Solution
3y + 5y = 8y
-y 2 + -y 2 = - 2y 2

### Complexity=7, Mode=with-exp

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
12y 2 + 4 - 7 + 3x - 4y - 3y + 4y
Simplified:
Solution
4 + - 7 = - 3
- 4y + - 3y + 4y = - 3y
24x 2 + x 2 + 4y 2 + 4y + 7 + 3x + 2
Simplified:
Solution
4x 2 + x 2 = 5x 2
7 + 2 = 9

### Complexity=2, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
1-(1 + 3y) + 2(2y - 3)
Simplified:
Solution
Apply the distributive property to each term.
-(1 + 3y) → - 1 - 3y
2(2y - 3) → 4y - 6

Now combine like terms
- 1 + - 6 = - 7
- 3y + 4y = 1y

2-(5y - 8) - 2(6 + 3)
Simplified:
Solution
Apply the distributive property to each term.
-(5y - 8) → - 5y + 8
- 2(3 + 6) → - 18

Now combine like terms
8 + - 18 = - 10

### Complexity=3, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
11(- 2y + 3x) - 2(2 - 5) - 2(8 + 7)
Simplified:
Solution
Apply the distributive property to each term.
1(- 2y + 3x) → - 2y + 3x
- 2(- 5 + 2) → 6
- 2(7 + 8) → - 30

Now combine like terms
6 + - 30 = - 24

Answer: 3x - 2y - 24

2-(5 + 6) - (3x + 3y) - 4(- 6 - 7)
Simplified:
Solution
Apply the distributive property to each term.
-(5 + 6) → - 11
-(3y + 3x) → - 3y - 3x
- 4(- 7 - 6) → 52

Now combine like terms
- 11 + 52 = 41

Answer: - 3x - 3y + 41

### Complexity=4, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
1-(5 - 4y) - (- 3y - 2) - (- 5y + 5) - 3(- 4x - 2)
Simplified:
Solution
Apply the distributive property to each term.
-(5 - 4y) → - 5 + 4y
-(- 3y - 2) → 3y + 2
-(- 5y + 5) → 5y - 5
- 3(- 4x - 2) → 12x + 6

Now combine like terms
- 5 + 2 + - 5 + 6 = - 2
4y + 3y + 5y = 12y

Answer: 12x + 12y - 2

22(- 4y + 2y) - (5x - 2y) - (7 - 3) - (2x - x)
Simplified:
Solution
Apply the distributive property to each term.
2(- 4y + 2y) → - 4y
-(- 2y + 5x) → 2y - 5x
-(- 3 + 7) → - 4
-(2x - x) → -x

Now combine like terms
- 4y + 2y = - 2y
- 5x + -x = - 6x

Answer: - 6x - 2y - 4

### Complexity=5, Mode=with-parens

Simplify the expression and order your answer based on alphabetical letter and magnitude. For x2, type x^2. Sample Answers: 3x + y - 3,   2x - 4y + 4,   x - y2 - 2y + 3 (type as: x - y^2 - 2y + 3)
13(5y - 4) - (- 4x - y) + 1(2x + 1) - (4y - 4y) + 1(-x - 4y)
Simplified:
Solution
Apply the distributive property to each term.
3(5y - 4) → 15y - 12
-(- 4x - y) → 4x + y
1(1 + 2x) → 1 + 2x
-(4y - 4y) → 0
1(-x - 4y) → -x - 4y

Now combine like terms
15y + y + - 4y = 12y
- 12 + 1 = - 11
4x + 2x + -x = 5x

Answer: 5x + 12y - 11

2- 4(-y - 5x) + 1(2y - 2y) - 2(- 5x + 3) + 4(- 4x - 3) - (3 + 3)
Simplified:
Solution
Apply the distributive property to each term.
- 4(-y - 5x) → 4y + 20x
1(2y - 2y) → 0
- 2(3 - 5x) → - 6 + 10x
4(- 4x - 3) → - 16x - 12
-(3 + 3) → - 6

Now combine like terms
20x + 10x + - 16x = 14x
- 6 + - 12 + - 6 = - 24

Answer: 14x + 4y - 24